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reorganized files
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V. Ferreira
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#ifndef POISSON_PROBLEM_HPP
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#define POISSON_PROBLEM_HPP
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#include <fstream>
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#include <iostream>
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#include <deal.II/base/quadrature_lib.h>
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#include <deal.II/base/logstream.h>
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#include <deal.II/base/tensor.h>
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#include <deal.II/base/utilities.h>
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#include <deal.II/base/index_set.h>
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#include <deal.II/lac/vector.h>
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#include <deal.II/lac/full_matrix.h>
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#include <deal.II/lac/sparse_matrix.h>
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#include <deal.II/lac/dynamic_sparsity_pattern.h>
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#include <deal.II/lac/solver_cg.h>
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#include <deal.II/lac/precondition.h>
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#include <deal.II/lac/affine_constraints.h>
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#include <deal.II/grid/tria.h>
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#include <deal.II/grid/grid_generator.h>
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#include <deal.II/grid/grid_tools.h>
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#include <deal.II/dofs/dof_handler.h>
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#include <deal.II/dofs/dof_tools.h>
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#include <deal.II/dofs/dof_renumbering.h>
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#include <deal.II/fe/fe_q.h>
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#include <deal.II/fe/fe_values.h>
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#include <deal.II/numerics/data_out.h>
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#include <deal.II/numerics/vector_tools.h>
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#include "parameters.hpp"
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#include "fields.hpp"
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using namespace dealii;
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// =-=-=-=-= Poisson Solver =-=-=-=-=
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template <int dim>
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class PoissonProblem
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{
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public:
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PoissonProblem(unsigned int degree, unsigned int Nv);
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void run();
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void set_Nv(unsigned int new_Nv);
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private:
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void create_mesh();
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void setup_system();
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void assemble_system();
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void solve();
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void output_results() const;
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Triangulation<dim> triangulation;
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FE_Q<dim> fe;
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DoFHandler<dim> dof_handler;
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AffineConstraints<double> constraints;
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SparsityPattern sparsity_pattern;
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SparseMatrix<double> system_matrix;
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Vector<double> solution; // phi
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Vector<double> system_rhs;
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MappingQ<dim> mapping;
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unsigned int Nv;
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};
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template <int dim>
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void PoissonProblem<dim>::set_Nv(unsigned int new_Nv)
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{
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Nv = new_Nv;
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}
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template <int dim>
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PoissonProblem<dim>::PoissonProblem(unsigned int degree, unsigned int Nv)
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: fe(degree)
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, dof_handler(triangulation)
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, mapping(degree)
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, Nv(Nv)
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{}
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// =-=-=-=-= Make Grid =-=-=-=-=
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template<int dim>
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void PoissonProblem<dim>::create_mesh()
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{
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GridGenerator::hyper_cube(triangulation,
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Parameters::X_DOMAIN_LEFT,
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Parameters::X_DOMAIN_RIGHT);
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// Make x-dim boundaries periodic
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Tensor<1, dim> offset;
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std::vector<GridTools::PeriodicFacePair<
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typename Triangulation<dim>::cell_iterator>> periodicity_vector;
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GridTools::collect_periodic_faces(triangulation,
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0,
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1,
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0,
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periodicity_vector,
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offset);
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triangulation.add_periodicity(periodicity_vector);
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triangulation.refine_global(Parameters::GLOBAL_REFINEMENT);
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}
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template <int dim>
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void PoissonProblem<dim>::setup_system()
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{
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dof_handler.distribute_dofs(fe);
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constraints.clear();
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DoFTools::make_hanging_node_constraints(dof_handler, constraints);
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// 'boundary' condition phi(x_0) = 0
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constraints.add_line(0);
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constraints.set_inhomogeneity(0, 0.0);
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constraints.close();
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DynamicSparsityPattern dsp(dof_handler.n_dofs());
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DoFTools::make_sparsity_pattern(dof_handler, dsp, constraints);
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sparsity_pattern.copy_from(dsp);
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system_matrix.reinit(sparsity_pattern);
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solution.reinit(dof_handler.n_dofs());
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system_rhs.reinit(dof_handler.n_dofs());
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}
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// =-=-=-=-= E_field = -dPhi/dx =-=-=-=-=
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template <int dim>
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class ElectricFieldPostprocessor : public DataPostprocessorVector<dim>
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{
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public:
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ElectricFieldPostprocessor()
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: DataPostprocessorVector<dim>("electric_field", update_gradients)
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{}
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virtual void evaluate_scalar_field(
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const DataPostprocessorInputs::Scalar<dim> &input_data,
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std::vector<Vector<double>> &computed_quantities) const override
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{
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AssertDimension(input_data.solution_gradients.size(),
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computed_quantities.size());
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for (unsigned int p = 0; p < input_data.solution_gradients.size(); ++p)
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{
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AssertDimension(computed_quantities[p].size(), dim);
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for (unsigned int d = 0; d < dim; ++d)
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computed_quantities[p][d] = -input_data.solution_gradients[p][d];
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}
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}
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};
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// =-=-=-=-= Poisson equation solver =-=-=-=-=
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template <int dim>
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void PoissonProblem<dim>::assemble_system()
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{
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QGauss<dim> quadrature_formula(fe.degree + 1);
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FEValues<dim> fe_values(fe, quadrature_formula,
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update_values |
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update_gradients |
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update_quadrature_points |
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update_JxW_values);
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const unsigned int dofs_per_cell = fe.n_dofs_per_cell();
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const unsigned int n_q_points = quadrature_formula.size();
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FullMatrix<double> cell_matrix(dofs_per_cell, dofs_per_cell);
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Vector<double> cell_rhs(dofs_per_cell);
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std::vector<types::global_dof_index> local_dof_indices(dofs_per_cell);
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ChargeDensity<dim> rhs_function(Parameters::EPS, Parameters::WAVE_NR, Nv);
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for (const auto &cell : dof_handler.active_cell_iterators())
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{
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fe_values.reinit(cell);
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cell_matrix = 0;
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cell_rhs = 0;
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for (unsigned int q = 0; q < n_q_points; ++q)
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{
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const double rho = rhs_function.value(fe_values.quadrature_point(q));
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for (unsigned int i = 0; i < dofs_per_cell; ++i)
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{
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for (unsigned int j = 0; j < dofs_per_cell; ++j)
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cell_matrix(i, j) +=
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fe_values.shape_grad(i, q) *
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fe_values.shape_grad(j, q) *
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fe_values.JxW(q);
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cell_rhs(i) +=
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fe_values.shape_value(i, q) *
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rho *
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fe_values.JxW(q);
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}
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}
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cell->get_dof_indices(local_dof_indices);
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constraints.distribute_local_to_global(cell_matrix,
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cell_rhs,
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local_dof_indices,
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system_matrix,
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system_rhs);
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}
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}
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template <int dim>
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void PoissonProblem<dim>::solve()
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{
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SolverControl solver_control(1000, 1e-12);
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SolverCG<Vector<double>> solver(solver_control);
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PreconditionSSOR<SparseMatrix<double>> preconditioner;
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preconditioner.initialize(system_matrix, 1.2);
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solver.solve(system_matrix, solution, system_rhs, preconditioner);
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constraints.distribute(solution);
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}
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template <int dim>
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void PoissonProblem<dim>::output_results() const
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{
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// --- extract DoF coordinates ---
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std::vector<Point<dim>> support_points(dof_handler.n_dofs());
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DoFTools::map_dofs_to_support_points(mapping,
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dof_handler,
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support_points);
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Vector<double> x_coordinate(dof_handler.n_dofs());
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for (unsigned int i = 0; i < support_points.size(); ++i)
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x_coordinate[i] = support_points[i][0]; // x-component in 1D
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//---- Output density ----
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ChargeDensity<dim> rho(Parameters::EPS, Parameters::WAVE_NR, Nv);
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DataOut<dim> data_out_rho;
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data_out_rho.attach_dof_handler(dof_handler);
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Vector<double> density(solution.size());
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VectorTools::interpolate(dof_handler, rho, density);
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data_out_rho.add_data_vector(density, "density");
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data_out_rho.add_data_vector(x_coordinate, "x_coordinate");
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data_out_rho.build_patches();
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std::ofstream out1("density.vtk");
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data_out_rho.write_vtk(out1);
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//---- Output electric field & potential ----
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DataOut<dim> data_out_E;
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data_out_E.attach_dof_handler(dof_handler);
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ElectricFieldPostprocessor<dim> electric_field;
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Vector<double> dummy(solution.size() * dim);
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data_out_E.add_data_vector(solution, "potential");
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data_out_E.add_data_vector(solution, electric_field);
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data_out_E.add_data_vector(x_coordinate, "x_coordinate");
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data_out_E.build_patches();
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std::ofstream out2("electric_field.vtk");
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data_out_E.write_vtk(out2);
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}
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template <int dim>
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void PoissonProblem<dim>::run()
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{
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create_mesh();
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setup_system();
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assemble_system();
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solve();
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output_results();
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}
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#endif
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